Branch-and-Bound Methods: General Formulation and Properties

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Abstract
The branch-and-bound procedure is formulated in rather general terms and necessary conditions for the branching and bounding functions are precisely specified. Results include the standard properties for finite procedures, plus several convergence conditions for infinite procedures. Discrete programming which includes integer programming and combinatorial optimization problems, is discussed and Fibonacci search is presented as an example of a nonfinite branch-and-bound procedure employing an optimal convergence rule.